Statistics and Probability Answers

Given a sample size of 65, with sample mean 726.2 and sample standard deviation 85.3,
we perform the following hypothesis test.
0 H :  750
1 H :  750
What is the conclusion of the test at the   0.10 level? Explain your answer.

Ten participants in a physical fitness program had their fasting blood sugar
levels taken at the start of the program. They were taken again on day 21.
The readings are given in the table below.

Start 105 94 107 111 109 111 102 124 109 102
Day 21 92 108 104 102 93 85 93 BB 103 90

It has been conjectured that the physical fitness program will lower the mean

level. I have included two sets of possible output for the test. Assume both
sets of measurements come from Normal populations. Tell which you would
choose as the appropriate one and why. write down the hypotheses and
level of significance for the test at the 5% level. Then give your decision and
conclusion.

A study was conducted to determine the adaptive significance of flower colour
in the scarlet gilia. The question is whether red of white flowered plants are
more attractive to the hummingbird pollinator. The numbers of fruit set in
flowers of the two colours was collected and is given in the following table.
Red White Totals
Fruit Set Yes 85 140 225
No 575 665 1240
Totals 660 805 1465

Below is the output for a X2 test of association.

Chi-Square Test: C17, C18

Expected counts are prjnted below observed counts
Chi-Square contributions are printed below expected counts

CI1 ClB Total
1 85 140 225


101.31 L23.63
2 .642 2 .166
2 515 555 1240

558.63 687.31
0.419 0.393
Totaf 660 805 1465

Chi-Sq : 5.681, DF : I, P-Value 0.017

a) Give the null and alternate hypotheses for a test of association. l2l

b) Tell how the expected value of 101 .37 for the number setting fruit in red
flowers was obtained, not simply the calculation but why it is done that
way, in other words, how it is related

An ecologist studied the habitat of a marine reef fish, the six bar wrasse
(Thalassomahardwicke), near an island in French Polynesia. She examined 48 patch
reef settlements at each of two distances from the reef crest: 250 metres and 800
metres. For each patch reef, she calculated the 'settler density', the number of settlers
or juvenile fish per unit of settlement habitat. Before collecting the data, she
hypothesised that the settler density might decrease as distance from the reef
increased, since the way the waves break over the reef crest causes resources (eg.
Food) to tend to decrease as distance from the reefcrest increases.
a. From the normality plots, argue that a t test should be run on this data. l2l
b. Present an argument for which of the three test outputs we should use to test
the ecologist's hypothesis.
c. Perform the test, making sure you include all steps.

If I roll 5 dice, what are the odds of getting AT LEAST 3 even numbers?

If its not too much trouble I'd love to know how you arrived at the answer, thanks.

what is the probability of a player getting all the four aces, when playing cards are uniformly distributed among the four players?

compute standard error of estimate for data below
x values= 3,-2,2,5,10
y values= 4,6,-2,0,-3

2. A Nationwide auto insurance manager wants to estimate the proportion of car owners, in a new market area, who purchase at least $1 million of liability coverage in their automobile insurance policies.
a. How large a sample should be chosen to estimate the proportion with a 95% error margin of 0.08?
Suppose the proportion is known to be about p_o=0.15.
b. How large a sample should be chosen to estimate the proportion with a 95% error margin of 0.08 if nothing is known about its value?

Whe en do we say "variances of the two samples are equal and not equal"? How do we know whether the variances of two samples are equal or not?

An oil company is planning to drill three exploratory wells. the company extimates that each well, independent of each other, has a 30% chance of being successful.

Find the proability distribution of X, the number of oil wells that will be successful.

Suppose the first well to be completed is successful, what is the probability that one of the two remaining wells is successful?